Gamma-ray bursts in 1.8 < z < 5.6 suggest that the time variation of the dark energy is small

We calibrated the peak energy–peak luminosity relation of gamma-ray bursts (GRBs; the so-called Yonetoku relation) using 33 events with redshift z < 1.62 without assuming any cosmological models. The luminosity distances to GRBs are estimated from those of large numbers of Type Ia supernovae with z < 1.755. This calibrated Yonetoku relation can be used as a new cosmic distance ladder towards higher redshifts. We determined the luminosity distances of 30 GRBs in 1.8 < z < 5.6 using the calibrated relation, and plotted the likelihood contour in the (Ωm, ΩΛ) plane. We obtained (Ωm, ΩΛ) = (0.37+0.14−0.11, 0.63+0.11−0.14) for a flat universe. Because our method is free from the circularity problem, we can say that our universe in 1.8 < z < 5.6 is compatible with the so-called concordance cosmological model derived for z < 1.8. This suggests that the time variation of the dark energy is small or zero up to z∼ 6.